The two banks have lagged behind Wells Fargo and J.P. Morgan on certain metrics, including dividends, share-price gains and valuation

There is a $24 billion reason why Bank of America Corp. and Citigroup Inc. shareholders should care about bank “stress tests,” results of which are expected this week.

That figure is the additional money combined the two banks theoretically could have returned to shareholders over the past three years if their levels of dividends and share buybacks were similar to those of Wells Fargo & Co., according to Wall Street Journal calculations. That they weren’t is partly due to the annual stress tests administered by the Federal...